%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SEU267+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n003.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 14:49:47 EDT 2022 % Result : Theorem 0.19s 0.46s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU267+1 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.34 % Computer : n003.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jun 19 10:03:28 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.46 % SZS status Theorem % 0.19/0.46 (* PROOF-FOUND *) % 0.19/0.46 (* BEGIN-PROOF *) % 0.19/0.46 % SZS output start Proof % 0.19/0.46 1. ((ordered_pair T_0 T_1) != (ordered_pair T_0 T_1)) ### Refl(=) % 0.19/0.46 2. (-. (Ex C, ((ordered_pair T_0 T_1) = (ordered_pair T_0 C)))) ### NotExists 1 % 0.19/0.46 3. (-. (Ex B, (Ex C, ((ordered_pair T_0 T_1) = (ordered_pair B C))))) ### NotExists 2 % 0.19/0.46 4. ((pair_first (ordered_pair T_0 T_1)) != (pair_first (ordered_pair T_0 T_1))) ### Refl(=) % 0.19/0.46 5. ((ordered_pair T_0 T_1) != (ordered_pair T_0 T_1)) ### Refl(=) % 0.19/0.46 6. ((pair_first (ordered_pair T_0 T_1)) != T_0) ((pair_first (ordered_pair T_0 T_1)) = T_0) ### Axiom % 0.19/0.46 7. (((ordered_pair T_0 T_1) = (ordered_pair T_0 T_1)) => ((pair_first (ordered_pair T_0 T_1)) = T_0)) ((pair_first (ordered_pair T_0 T_1)) != T_0) ### Imply 5 6 % 0.19/0.46 8. (All D, (((ordered_pair T_0 T_1) = (ordered_pair T_0 D)) => ((pair_first (ordered_pair T_0 T_1)) = T_0))) ((pair_first (ordered_pair T_0 T_1)) != T_0) ### All 7 % 0.19/0.46 9. (All C, (All D, (((ordered_pair T_0 T_1) = (ordered_pair C D)) => ((pair_first (ordered_pair T_0 T_1)) = C)))) ((pair_first (ordered_pair T_0 T_1)) != T_0) ### All 8 % 0.19/0.46 10. (((pair_first (ordered_pair T_0 T_1)) = (pair_first (ordered_pair T_0 T_1))) <=> (All C, (All D, (((ordered_pair T_0 T_1) = (ordered_pair C D)) => ((pair_first (ordered_pair T_0 T_1)) = C))))) ((pair_first (ordered_pair T_0 T_1)) != T_0) ### Equiv 4 9 % 0.19/0.46 11. (All B, ((B = (pair_first (ordered_pair T_0 T_1))) <=> (All C, (All D, (((ordered_pair T_0 T_1) = (ordered_pair C D)) => (B = C)))))) ((pair_first (ordered_pair T_0 T_1)) != T_0) ### All 10 % 0.19/0.46 12. ((Ex B, (Ex C, ((ordered_pair T_0 T_1) = (ordered_pair B C)))) => (All B, ((B = (pair_first (ordered_pair T_0 T_1))) <=> (All C, (All D, (((ordered_pair T_0 T_1) = (ordered_pair C D)) => (B = C))))))) ((pair_first (ordered_pair T_0 T_1)) != T_0) ### Imply 3 11 % 0.19/0.46 13. (All A, ((Ex B, (Ex C, (A = (ordered_pair B C)))) => (All B, ((B = (pair_first A)) <=> (All C, (All D, ((A = (ordered_pair C D)) => (B = C)))))))) ((pair_first (ordered_pair T_0 T_1)) != T_0) ### All 12 % 0.19/0.46 14. ((pair_second (ordered_pair T_0 T_1)) != (pair_second (ordered_pair T_0 T_1))) ### Refl(=) % 0.19/0.46 15. ((ordered_pair T_0 T_1) != (ordered_pair T_0 T_1)) ### Refl(=) % 0.19/0.46 16. ((pair_second (ordered_pair T_0 T_1)) != T_1) ((pair_second (ordered_pair T_0 T_1)) = T_1) ### Axiom % 0.19/0.46 17. (((ordered_pair T_0 T_1) = (ordered_pair T_0 T_1)) => ((pair_second (ordered_pair T_0 T_1)) = T_1)) ((pair_second (ordered_pair T_0 T_1)) != T_1) ### Imply 15 16 % 0.19/0.46 18. (All D, (((ordered_pair T_0 T_1) = (ordered_pair T_0 D)) => ((pair_second (ordered_pair T_0 T_1)) = D))) ((pair_second (ordered_pair T_0 T_1)) != T_1) ### All 17 % 0.19/0.46 19. (All C, (All D, (((ordered_pair T_0 T_1) = (ordered_pair C D)) => ((pair_second (ordered_pair T_0 T_1)) = D)))) ((pair_second (ordered_pair T_0 T_1)) != T_1) ### All 18 % 0.19/0.46 20. (((pair_second (ordered_pair T_0 T_1)) = (pair_second (ordered_pair T_0 T_1))) <=> (All C, (All D, (((ordered_pair T_0 T_1) = (ordered_pair C D)) => ((pair_second (ordered_pair T_0 T_1)) = D))))) ((pair_second (ordered_pair T_0 T_1)) != T_1) ### Equiv 14 19 % 0.19/0.46 21. (All B, ((B = (pair_second (ordered_pair T_0 T_1))) <=> (All C, (All D, (((ordered_pair T_0 T_1) = (ordered_pair C D)) => (B = D)))))) ((pair_second (ordered_pair T_0 T_1)) != T_1) ### All 20 % 0.19/0.46 22. ((Ex B, (Ex C, ((ordered_pair T_0 T_1) = (ordered_pair B C)))) => (All B, ((B = (pair_second (ordered_pair T_0 T_1))) <=> (All C, (All D, (((ordered_pair T_0 T_1) = (ordered_pair C D)) => (B = D))))))) ((pair_second (ordered_pair T_0 T_1)) != T_1) ### Imply 3 21 % 0.19/0.46 23. (All A, ((Ex B, (Ex C, (A = (ordered_pair B C)))) => (All B, ((B = (pair_second A)) <=> (All C, (All D, ((A = (ordered_pair C D)) => (B = D)))))))) ((pair_second (ordered_pair T_0 T_1)) != T_1) ### All 22 % 0.19/0.46 24. (-. (((pair_first (ordered_pair T_0 T_1)) = T_0) /\ ((pair_second (ordered_pair T_0 T_1)) = T_1))) (All A, ((Ex B, (Ex C, (A = (ordered_pair B C)))) => (All B, ((B = (pair_second A)) <=> (All C, (All D, ((A = (ordered_pair C D)) => (B = D)))))))) (All A, ((Ex B, (Ex C, (A = (ordered_pair B C)))) => (All B, ((B = (pair_first A)) <=> (All C, (All D, ((A = (ordered_pair C D)) => (B = C)))))))) ### NotAnd 13 23 % 0.19/0.46 25. (-. (All B, (((pair_first (ordered_pair T_0 B)) = T_0) /\ ((pair_second (ordered_pair T_0 B)) = B)))) (All A, ((Ex B, (Ex C, (A = (ordered_pair B C)))) => (All B, ((B = (pair_first A)) <=> (All C, (All D, ((A = (ordered_pair C D)) => (B = C)))))))) (All A, ((Ex B, (Ex C, (A = (ordered_pair B C)))) => (All B, ((B = (pair_second A)) <=> (All C, (All D, ((A = (ordered_pair C D)) => (B = D)))))))) ### NotAllEx 24 % 0.19/0.46 26. (-. (All A, (All B, (((pair_first (ordered_pair A B)) = A) /\ ((pair_second (ordered_pair A B)) = B))))) (All A, ((Ex B, (Ex C, (A = (ordered_pair B C)))) => (All B, ((B = (pair_second A)) <=> (All C, (All D, ((A = (ordered_pair C D)) => (B = D)))))))) (All A, ((Ex B, (Ex C, (A = (ordered_pair B C)))) => (All B, ((B = (pair_first A)) <=> (All C, (All D, ((A = (ordered_pair C D)) => (B = C)))))))) ### NotAllEx 25 % 0.19/0.46 % SZS output end Proof % 0.19/0.46 (* END-PROOF *) %------------------------------------------------------------------------------